Q. 284.5( 17 Votes )

The 8th term of an AP is zero. Prove that its 38th term is triple its 18th term.

Answer :

Let a be the first term and d be the common difference.

Given: a8 = 0


To prove: a38 = 3 × a18


Now, Consider a8 = 0


a + (8 - 1)d = 0


a + 7d = 0


a = - 7d ……. (1)


Consider a38 = a + (38 - 1)d


a38 = - 7d + 37d (from equation (1))


a38 = 30d ………. (2)


Now, consider a18 = a + (18 - 1)d


a18 = - 7d + 17d (from equation (1))


a18 = 10d ……….(3)


From equation (2) and (3), we get,


a38 = 3 × a18


Hence, proved.


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